Problem: Simplify the following expression: $ p = -9 + \dfrac{9x}{-6x + 4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6x + 4}{-6x + 4}$ $ \dfrac{-9}{1} \times \dfrac{-6x + 4}{-6x + 4} = \dfrac{54x - 36}{-6x + 4} $ Therefore $ p = \dfrac{54x - 36}{-6x + 4} + \dfrac{9x}{-6x + 4} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{54x - 36 + 9x}{-6x + 4} $ $p = \dfrac{63x - 36}{-6x + 4}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-63x + 36}{6x - 4}$